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Maths

Mental Maths: Efficient Calculation Strategies

Overview

Students move beyond written methods to develop a toolkit of flexible mental strategies, understanding that the best method depends on the specific numbers involved.

Learning Objective
Students learn and apply multiple mental calculation strategies (compensating, near doubles, partitioning, bridging through 10/100) and choose the most efficient method for a given calculation.

Resources needed

  • Mini whiteboards
  • No other materials needed

Lesson stages

0 / 7 done
  1. 1 Write 99 + 47 on the board. Collect methods from students. Likely: column addition (slow), 100+47−1=146 (compensating), 47+47+52 (near double-ish), 99+40+7 (partitioning). 'Which is fastest? Why?'
  2. 2 Add or subtract a round number, then adjust. 99+47 = 100+47−1 = 146. 198+63 = 200+63−2 = 261. 76−29 = 76−30+1 = 47. Students practise six compensating examples. Key: always adjust in the right direction.
  3. 3 Split numbers to make them easier. 46+37 = 40+6+30+7 = 70+13 = 83. Or: 46+37 = 46+30+7 = 76+7 = 83. 'Which partitioning method do you prefer? Does it matter?' Students try both for three calculations.
  4. 4 If you know double 36 = 72, then 36+37 = 72+1 = 73. 35+37 = double 36 + 1 = 73. Students identify near double pairs and solve quickly.
  5. 5 87+34: bridge through 100. 87+13=100, then add remaining 21. Answer: 121. Students practise with numbers close to 100, 200, 1000.
  6. 6 Display 10 calculations. Students choose their method and record it alongside their answer. Share: 'What method did you choose for 201−98? Why?' Discuss how different people may choose different but equally valid strategies.
  7. 7 Teams of four: one person calls a calculation, others find the answer mentally, first to show the correct answer on a whiteboard wins a point. No written methods allowed.

Tap a step to mark it as done.

Variations

  • Extend to 3-digit multiplication strategies (e.g. 16×25 = 4×100 = 400)
  • Apply strategies to decimals (e.g. 3.9+4.7)
  • Discuss when written methods ARE more efficient than mental ones
More information

Display strategy names: compensating, partitioning, bridging, near doubles. Encourage students to explain their thinking in full sentences.

Focus on one strategy at a time. Allow jottings (not full written methods) for those who need them. Reduce the size of numbers.

Are students choosing efficient methods (not always the same one)? Can they explain why they chose a particular strategy? Are their answers accurate?

Fully equipment-free — only requires students and a voice. Mini whiteboards can be replaced with paper scraps.

Students may use compensating but adjust in the wrong direction (adding when they should subtract). Reinforce: 'I added too much, so I need to subtract the extra.'

Activity details
Primary Medium 30 minutes No prep Solo, Pairs, Whole Class Indoor & Outdoor
Topics
Mental Calculation Strategies Number Sense Arithmetic